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A Course in Financial Calculus

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  • Etheridge,Alison

Abstract

Finance provides a dramatic example of the successful application of advanced mathematical techniques to the practical problem of pricing financial derivatives. This self-contained 2002 text is designed for first courses in financial calculus aimed at students with a good background in mathematics. Key concepts such as martingales and change of measure are introduced in the discrete time framework, allowing an accessible account of Brownian motion and stochastic calculus: proofs in the continuous-time world follow naturally. The Black-Scholes pricing formula is first derived in the simplest financial context. The second half of the book is then devoted to increasing the financial sophistication of the models and instruments. The final chapter introduces more advanced topics including stock price models with jumps, and stochastic volatility. A valuable feature is the large number of exercises and examples, designed to test technique and illustrate how the methods and concepts can be applied to realistic financial questions.

Suggested Citation

  • Etheridge,Alison, 2002. "A Course in Financial Calculus," Cambridge Books, Cambridge University Press, number 9780521813853.
    • Handle: RePEc:cup:cbooks:9780521813853
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    Citations

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    Cited by:

    1. Zhongkai Liu & Tao Pang, 2016. "An efficient grid lattice algorithm for pricing American-style options," International Journal of Financial Markets and Derivatives, Inderscience Enterprises Ltd, vol. 5(1), pages 36-55.
    2. Diderik Lund, 2005. "How to analyze the investment–uncertainty relationship in real option models?," Review of Financial Economics, John Wiley & Sons, vol. 14(3-4), pages 311-322.
    3. Lars Tyge Nielsen, 2023. "A Counterexample in Ito Integration Theory," Papers 2305.10695, arXiv.org.
    4. Chung-Han Hsieh, 2022. "On Robustness of Double Linear Trading with Transaction Costs," Papers 2209.12383, arXiv.org.
    5. Jason S. Anquandah & Leonid V. Bogachev, 2019. "Optimal Stopping and Utility in a Simple Model of Unemployment Insurance," Papers 1902.06175, arXiv.org, revised Sep 2019.
    6. Boonman, Hettie J. & Siddiqui, Afzal S., 2017. "Capacity optimization under uncertainty: The impact of operational time lags," European Journal of Operational Research, Elsevier, vol. 262(2), pages 660-672.
    7. Xin-Yu Wang & Chung-Han Hsieh, 2023. "On Robustness of Double Linear Policy with Time-Varying Weights," Papers 2303.10806, arXiv.org.
    8. William T. Shaw, 2008. "A model of returns for the post-credit-crunch reality: Hybrid Brownian motion with price feedback," Papers 0811.0182, arXiv.org, revised Aug 2009.
    9. Martin Kegnenlezom & Patrice Takam Soh & Antoine-Marie Bogso & Yves Emvudu Wono, 2019. "European Option Pricing of electricity under exponential functional of L\'evy processes with Price-Cap principle," Papers 1906.10888, arXiv.org.
    10. Thompson, James R. & Wilson, James R., 2016. "Multifractal detrended fluctuation analysis: Practical applications to financial time series," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 126(C), pages 63-88.
    11. Bilgi Yilmaz, 2018. "Computation of option greeks under hybrid stochastic volatility models via Malliavin calculus," Papers 1806.06061, arXiv.org.
    12. Hung Nguyen & Uyen Pham & Hien Tran, 2012. "On some claims related to Choquet integral risk measures," Annals of Operations Research, Springer, vol. 195(1), pages 5-31, May.
    13. Alvaro Cartea & Marcelo Figueroa, 2005. "Pricing in Electricity Markets: A Mean Reverting Jump Diffusion Model with Seasonality," Applied Mathematical Finance, Taylor & Francis Journals, vol. 12(4), pages 313-335.
    14. Gareth O. Roberts & Jeffrey S. Rosenthal, 2019. "Hitting Time and Convergence Rate Bounds for Symmetric Langevin Diffusions," Methodology and Computing in Applied Probability, Springer, vol. 21(3), pages 921-929, September.
    15. Kim Changki, 2005. "Surrender Rate Impacts on Asset Liability Management," Asia-Pacific Journal of Risk and Insurance, De Gruyter, vol. 1(1), pages 1-36, June.
    16. Roger MERCKEN & Lisette MOTMANS & Ghislain HOUBEN, 2010. "No more replicating portfolios : a simple convex combination to understand the risk-neutral valuation method for the multi-step binomial valuation of a call option," EuroEconomica, Danubius University of Galati, issue 24, pages 64-71, March.
    17. Alexander Kushpel, 2015. "Pricing of high-dimensional options," Papers 1510.07221, arXiv.org.
    18. Jason S. Anquandah & Leonid V. Bogachev, 2019. "Optimal Stopping and Utility in a Simple Modelof Unemployment Insurance," Risks, MDPI, vol. 7(3), pages 1-41, September.
    19. Brian A. Eales & Radu Tunaru, 2004. "Financial Engineering with Reverse Cliquet Options," Money Macro and Finance (MMF) Research Group Conference 2004 81, Money Macro and Finance Research Group.
    20. Stefanescu, Razvan & Dumitriu, Ramona, 2015. "Conţinutul analizei seriilor de timp financiare [The Essentials of the Analysis of Financial Time Series]," MPRA Paper 67175, University Library of Munich, Germany.
    21. William T. Shaw & Marcus Schofield, 2015. "A model of returns for the post-credit-crunch reality: hybrid Brownian motion with price feedback," Quantitative Finance, Taylor & Francis Journals, vol. 15(6), pages 975-998, June.

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